27213 - Mathematical Analysis 2

Course contents

Differential and integral calculus. 
The differential, Taylor's formula, implicit functions, local extrema, Lagrange multipliers, 
measure theory, the Lebesgue integral, surface integrals, the theorems of Gauss-Green, 
Gauss and Stokes.

Readings/Bibliography

Ermanno Lanconelli, Analisi Matematica 1 e 2, Ed. Pitagora.
Enrico Giusti, Analisi Matematica 1 e 2, Ed. Boringhieri.
Pagani, C.D.-Salsa, S., Analisi Matematica 1 e 2, Ed. Zanichelli. 

Teaching methods

Classroom lectures with exercises.

Assessment methods

The final examination involves a written test and an oral part. To sign up you should use the system AlmaEsami. For a schedule of examinations, please refer always to AlmaEsami. In the written test, the student has to solve some exercises to demonstrate that he has acquired and know how to use the tools provided during the course. It is evaluated through a judgment which should be positive to allow access to the oral examination. The validity of the written test is limited to the same exam session or at the next one. If the student takes a new written test, the previous one is canceled. Overcoming the written test allows to the oral examination, which consists of a discussion on the written test and in questions that tend to establish the theoretical knowledge of the course contents, the acquisition of the methodological rigor and the ability to reason about topics related to the course. The oral examination aims in particular to verify the achievement of the expected knowledge and skills, knowledge of a more informative character with a wider basic instrumentation to deal with the description of various physical phenomena, skills to solve problems of constrained maxima or minima, to study the convergence of integrals in more variables, to calculate surface integrals. Both the written and oral test have the additional purpose of verifying the learning of the general methods of mathematical analysis and the acquisition of critical judgment in relation to the solution of mathematical problems. The final score, out of thirty, takes into account the scores reported in both tests.

Office hours

See the website of Francesco Uguzzoni